Linear, Quadratic and Real-Life Graphs

Reading a straight line from its equation, sketching a parabola from its factors, and interpreting the graphs that describe journeys.

หลักสูตรแกนกลาง / สสวท.: จำนวนและพีชคณิต (Number and Algebra)ตรงกับ ม.3 บทที่ 5 กราฟของฟังก์ชันกำลังสอง
Common Core (US): 8.F, F-IF
Cambridge: Lower Secondary Stage 9 — Algebra: sequences, functions and graphs

7.1 Straight lines

Gradient and intercept

y = m x + c m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

$m$ is the gradient, $c$ the $y$ -intercept. Parallel lines share a gradient.

ตัวอย่าง

Find the equation of the line through $(2, 1)$ and $(6, 13)$ .

วิธีทำ

1. $m = \frac{13 - 1}{6 - 2} = 3$
2. $y = 3 x + c$ ; substitute $(2, 1)$ : $1 = 6 + c$ , so $c = - 5$
3.Check with $(6, 13)$ : $18 - 5 = 13$

ตอบ $y = 3 x - 5$

เคล็ดลับ

Solving simultaneous equations graphically is exactly this in reverse: draw both lines and read off where they cross. The algebra gives an exact answer, the graph a picture of why there is one.

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